How do I achieve a particle trail effect?
I think it can be done.

Unfortunately it requires skill. 

In this example I used a sphere emitter
and a slightly smaller sphere that had collision physics enables, dynamic painting as a canvas, and a negative strength force field to attract the particles.

The slightly larger emitting sphere isnt rendered, and the render starts after the particles were alive for about 100 frames and had enough time to settle and get going.

So the emitter would drop all the particles and the colliding sphere would attract them and get dynamically painted on its surface.

to make the particles move on the surface, I made three vortex forces. Although in your example it looks like there are six, plus two forces(one on top one on bottom)

I also saw that your example had lots of compositing done ontop of it so I attempted a transition to a bokeh blur...
Have next to zero experience with compositing atm.



Here is the file 
But you will need to re-bake the canvas for dynamic painting and set the timeline to start at frame 1.

P.S. temporarily make the particle scale(in particle panel) super tiny before dynamic painting or else you will get super wide paint marks.